A multi-tier adaptive grid algorithm for the evolutionary multi-objective optimisation of complex problems

The multi-tier Covariance Matrix Adaptation Pareto Archived Evolution Strategy (m-CMA-PAES) is an evolutionary multi-objective optimisation (EMO) algorithm for real-valued optimisation problems. It combines a nonelitist adaptive grid based selection scheme with the efficient strategy parameter adaptation of the elitist CovarianceMatrix Adaptation Evolution Strategy (CMA-ES). In the original CMA-PAES, a solution is selected as a parent for the next population using an elitist adaptive grid archiving (AGA) scheme derived from the Pareto Archived Evolution Strategy (PAES). In contrast, a multi-tiered AGA scheme to populate the archive using an adaptive grid for each level of non-dominated solutions in the considered candidate population is proposed. The new selection scheme improves the performance of the CMA-PAES as shown using benchmark functions from the ZDT, CEC09, and DTLZ test suite in a comparison against the (μ + λ) Multi-Objective Covariance Matrix Adaptation Evolution Strategy (MO-CMA-ES). In comparison with MO-CMA-ES, the experimental results show that the proposed algorithm offers up to a 69% performance increase according to the Inverse Generational Distance (IGD) metric.